Machine based on inertial rotational forces operating as a turbine or a pump

ABSTRACT

A machine based on rotational inertial forces operating as a turbine or a pump is described.  
     In accordance with the present invention the machine consists of the following components, to wit, (a) a mechanism made up of a crankshaft, crank and connecting rod designed to generate the oscillatory motion of the rotor R 1 , (b) a tube fastened to R 1  curved and closed on itself and communicating with an inlet S A  and an outlet S B  dividing the tube in two circuits C 1  C 1′  in such a manner that the surface area of their projection on a plane perpendicular to the oscillation axis of R 1  is equal, (c) four 2-way valves each inserted at each end of C 1  {overscore (f)} i &gt;{overscore (f)} e  and C 1′  and operated by a mechanism in which with to complete oscillation of R 1  corresponds a left-hand rotation of 360° of the cranks causing opening of the pair of valves of C 1  only in the interval θ(0°, 180°) and opening of the valves of C 1′  only in the interval θ(180°, 360°) with the origin of the angle θ being fixed so that for θ=0° there is a corresponding maximum left-hand velocity of the rotor and for θ=180° the maximum right-hand velocity. In this manner the liquid of C 1  develops a left-hand inertial force f 1  and the liquid of C 1′  an identical right-hand inertial force f 1′ . In addition both are oriented towards the cross section S A  to which is applied the external force f e  with opposite direction with the forces f i  increasing with the velocity of rotation of the cranks so that for a mean value f i  less than f e  the velocity of the liquid of C i  has a direction from S A  to S B  and the machine operates as a turbine while for the machine it operates as a pump.

[0001] The present invention relates to a machine based on rotational inertial forces operating as a turbine or a pump in accordance with the classifying part of claim 1.

[0002] The following description is divided in the following paragraphs:

[0003] A. characteristics and advantages of the turbopump,

[0004] B. construction details of the turbopump,

[0005] C. operation of the machine as a turbine or a pump,

[0006] D. valve opening and closing mechanism,

[0007] E. inertial forces employed in the liquid of the turbopump and balancing of the reactions transmitted to the supporting frame,

[0008] F. the turbopump connected to a filling tank and a drain tank,

[0009] G. control of the power exchanged between a motor and a user, and

[0010] H. claims.

[0011] A. Characteristics and Advantages of the Turbopump

[0012] 1. In operation of the machine as a turbine the latter with the increase of revolutions per second of the user shaft develops thereon a moment automatically decreasing continuously from a maximum to a null value. Therefore the machine can replace with great advantage the stepped velocity change controlled and based on toothed wheels.

[0013] 2. Change of the machine as a turbine or a pump is extremely simple because it is done only by changing the motor shaft rotation velocity or that of the user shaft.

[0014] 3. The machine's output is high. It is subject only to the hydraulic leaks due to the passage of the liquid in the tubes and to the mechanical leaks of the connecting shaft-connecting rod & crank system.

[0015] 4. When operating as a turbine the machine converts pressure energy subtracted from the liquid into mechanical energy yielded to the crankshaft. When operating as a pump the machine converts the mechanical energy absorbed from the crankshaft into liquid pressure energy.

[0016] 5. The hydraulic machine operating as a turbine develops on the crankshaft a moment decreasing with the increase in the number of rps of the user shaft by a maximum value for n=0 to a null value for n=n_(o). For n>n_(o), the machine operates as a pump. In this case the direction of the velocity of the resultant applied to the liquid contained in the active circuits and the pressure developed increases with (n²−n_(o) ²).

[0017] B. Construction Details of the Turbopump

[0018] In the patent description of the present application there are symbols, physical magnitudes, mathematical expressions and circuits identical to those used in the description of the patents EP0964161A1 and U.S. Pat. No. 6,395,917B1 of the pump based on identical rotational inertial forces.

[0019] A basic difference is the use instead of one-way valves in the machine described below of two-way valves which allow interesting applications described below.

[0020] In FIG. 1/5 the construction diagram of the turbopump is summarized. It consists of a rotor R₁ oscillating with a maximum rotation of ±φ₀ around the shaft 1 fastened to the supporting frame 7. The oscillation mechanism of R₁ consists of the connecting rod 3 whose small end is coupled to the piston pin 2 fastened at R₁ and with its big end coupled to the pin 4 of the crank 5. The latter is fastened to the crankshaft 6 parallel to the shaft 1 which rotates at angular velocity φ′=dφ/dt on bearings fastened to the supporting frame 7. To the rotor R₁ is rigidly fastened a hydraulic circuit consisting of a tube whose axis is curved around a circumference whose center belongs to the axis of the shaft 1 which is perpendicular to the plane of the circumference. To the tube are applied two apertures with cross section S_(A) and S_(B) having common axis A-B which has a point in common with the axis of the shaft 1.

[0021] The longitudinal axis of the tube is divided by the axis A-B in two semicircumferences corresponding to two active circuits designated C₁ and C₁. Each of the latter going from point B towards A has respectively a left-hand direction and a right-hand direction. At the ends of C₁ and C₁, there is inserted respectively the pair of identical two-way valves (V₁, V₁₁) and (V_(1′), V_(11′)) The two pairs are controlled mechanically so that the pair (V₁, V₁₁) and the pair (V_(1′), V_(11′)) are respectively open only in the interval θ(0°, 180°) and the interval θ(180°, 360°). With this arrangement the following advantages are secured: (a), independence of the two pairs (C₁, f₁) and (C_(1′), f_(1′)) where f₁ (respectively f_(1′)) is the force generated by the liquid of C₁ (C_(1′)) which in this manner can operate only in the respective circuit; (b) the two-wayness of the valves allows in each circuit a velocity of the liquid in two opposite directions and therefore a single machine can operate either as a turbine or a pump; c) transfer to the rotor of the kinetic energy of the liquid corresponding to its relative velocity with respect to the circuit at the moment of closing of the valves. It is noted that at C₁ for ν=180° and at C_(1′) for ν=360° the liquid respectively contained has the maximum relative velocities and therefore the closing of the valves causes a considerable impulse of moment on the crankshaft.

[0022] It is noted that the oscillation system by means of connecting rod and crank can, with the advantage of less encumbrance and saving of components, consist of the crankshaft 5 to which is fastened eccentrically a ball bearing whose external ring can rotate resting with close tolerance alternatively in the intervals θ(0°, 180°) and the interval θ(180°, 360°) only on one of the two parallel blades equidistant from the oscillation axis of R₁ to which they are welded.

[0023] It is also noted that the active circuit C_(i) (i=1, 1′) consisting of a semicircumference can also be realized by a circuit made up of a cylindrical or Archimedean spiral. The two active circuits C_(i) made from a cylindrical spiral with an uneven number of superimposed layers are made up of a whole number of turns to which is added a final half-turn. The 2-phase circuit is obtained by connecting the two half-turns of two identical circuits so that the two circuits C_(i) starting from their point of connection are wound with opposite rotation direction. The 2-phase circuit wound as an Archimedean spiral consists of two circuits C_(i) wound as Archimedean spirals which must be wound with opposite direction starting from the initial point. The cylindrical and Archimedean spiral windings are particularly suitable in high pressure cases.

[0024] C. Operation of the Machine as a Turbine or a Pump

[0025] It was established that in the interval θ(0°, 180°) only the valves of the circuit C₁ should be open where the left-hand force f₁ (FIG. 1/5) is developed and that in ν(180°, 360°) only the valves of the circuit C_(1′) where the right-hand force f_(1′) is developed should be open.

[0026] It was also established that the external force f_(e) should have direction from S_(A) to S_(B) (FIG. 1/5) and therefore it has a direction opposite to that of the inertial forces f₁ and f_(1′) developed in the circuits C_(1′) where i=1, 1^(′).

[0027] From the established conditions it follows that the series (f₁−f_(e)) causes acceleration of the mass m₀ of the liquid of C_(i) expressed by: $\begin{matrix} {\frac{d^{2}S_{i}}{{dt}^{2}} = {\frac{1}{m_{0}}\left( {{\overset{\_}{f}}_{i} - {\overset{\_}{f}}_{e}} \right)}} & \left. 1 \right) \end{matrix}$

[0028] From (1) is inferred the following value of the relative displacement of the liquid of the circuit C_(i) in θ(0°, 180°) and in θ(180°, 360°): $\begin{matrix} {{S\left( 180^{\circ} \right)} = {2\pi \quad \phi_{o}r_{o}\frac{n^{2} - n_{o}^{2}}{n_{2}}}} & (2) \end{matrix}$

[0029] where φ₀ is the maximum rotation angle of the rotor oscillatory motion to which corresponds the mean value {overscore (f)} and n₀ is the number of rotations per second of the crank to which corresponds the equalization {overscore (f)}_(i)={overscore (f)}_(e).

[0030] From (2) is inferred the mean value of the velocity of the circuit C_(i) in θ(0°, 180°) and θ(180°, 360°). $\begin{matrix} {{\overset{\_}{v}}_{c} = {{{nS}_{i}\left( 180^{\circ} \right)} = {2\pi \quad \phi_{o}r_{o}\frac{n^{2} - n_{o}^{2}}{n}}}} & (3) \end{matrix}$

[0031] from which is found the flow:

Q={overscore (ν)} _(c) S _(c)  (4)

[0032] For n<n₀ velocity {overscore (ν)}_(c) expressed by (3) has a right-hand direction opposite to that of f_(i) and the machine when operating as a turbine transfers to the rotor the power f_(i){overscore (ν)}_(c) yielded by the liquid of C_(i). For n>n_(o) the velocity {overscore (ν)}_(c) has the same direction as f_(i) and the machine when operating as a pump having a head of f_(e) takes from the rotor the power:

P _(fi)={overscore (ν)}_(c){overscore (f)}_(i)  (5)

[0033] which it transfers to the liquid of C_(i).

[0034] From the integration of (1) it follows that when operating as a turbine, for n<n_(o) the liquid of the circuit C_(1′) at closing angle θ=180° of its valve V₁ has a maximum relative velocity and direction identical to that of the rotor expressed by: $\begin{matrix} {{v_{c}\left( 180^{\circ} \right)} = {4\quad \pi \quad \phi_{o}r_{o}\frac{n^{2} - n_{o}^{2}}{n}}} & (6) \end{matrix}$

[0035] Accordingly the closing of the valve V₁ causes transmission to the rotor R₁ of the kinetic energy: $\begin{matrix} {E_{c} = {m_{o}\frac{v_{c}^{2}\left( 180^{\circ} \right)}{2}}} & (7) \end{matrix}$

[0036] The same phenomenon is repeated for the angle θ=360° at which upon closing of the valve V_(1′) there is transmission to R₁ having maximum velocity and direction identical to that of the liquid, of an identical E_(o) of the liquid of the circuit C_(1′). Accordingly the power developed by the liquid of the circuits for closing of the valves is: $\begin{matrix} {P_{CH} = {n\quad m_{o}\frac{v_{c}^{2}\left( 180^{\circ} \right)}{2}}} & (8) \end{matrix}$

[0037] For (5) an (8) it follows that the total power developed by the turbine is: $P = {{P_{fi} + P_{CH}} = {{{\overset{\_}{f}}_{i}{\overset{\_}{v}}_{c}} + {n\quad m_{o}\frac{v_{o}^{2}\left( 180^{\circ} \right)}{2}}}}$

[0038] Power P is transmitted to the rotor R₁ and to the crankshaft in accordance with the following equations:

P=P _(fi) +P _(CH) =P _(R1) =P _(MA)  (10)

[0039] where

P _(R1) =r ₀ {overscore (f)} _(R1){overscore (φ)}

[0040] in which F_(R1) is the mean value of the reaction caused on the rotor by the power P_(fi) and P_(CH) and {overscore (φ)} is the mean value of the angular velocity of R₁ in φ(0, φ₀).

[0041] In addition:

P _(MA) =r _(MA) {overscore (f)} _(MA)θ  (11)

[0042] where r_(MA) is the radius of the crank and {overscore (f)}_(MA) is the mean value of the reaction on the crank caused by the power P_(R1).

[0043] Similar phenomena take place in the operation of the machine as a pump at valve closing.

[0044] From the above relationships it is inferred that in operation of the machine as a turbine the mean value of the moment transmitted to the crankshaft a_(MA) and the user is due to the summation (P_(fi)+P_(CH))/θ′ which with change of the number of rps changes by a maximum value for n=0 to a value null for n=n_(o).

[0045] In addition said tendency occurs continuously and automatically and without the use of any particular device.

[0046] For n>n_(o) the machine operates as a pump developing the power expressed by P₁=nf_(i)S(180°). It displays the following advantages: (1) the pump has an upper limit of rps established only by the mechanical strength of its components and not due to functional motives as for example in the piston pump. In addition it has no preferred velocity like for example the centrifugal pump. (2) With the change in rps the pump develops a flow rate, pressure and power respectively increasing with:

[0047] n, n², n³ while the output tends to increase with n. Accordingly with variation of the rps it can vary its field of applicability in a broad range. 3) The pump furthermore has no mechanical components except the valves in contact with the liquid pumped and therefore with an appropriate choice of materials is particularly suited to pumping of dangerous and corrosive liquids.

[0048] D. Valve Opening and Closing Mechanism

[0049] The mechanism consists of (FIG. 2/5): (1) four shafts a₁(i=1, 2, 3, 4) rotating on bearings with vertical axis fastened in a central position to the side walls of the circuits C_(i); (2) toothing D₁ (i=1, 2, 3, 4) applied to the end of each shaft a_(i) in a position outside the circuit; (3) a closing and opening plate L_(i)(i=1, 2, 3, 4) each fastened to the corresponding shaft a_(L) within the corresponding circuit C_(i); and (4) two cylindrical segments 8 and 9 fastened to the supporting framework and on each of which are fastened two toothings d₁(i=1, 2, 3, 4) each of which can couple with the corresponding toothing D₁ only for one 90° rotation of the corresponding plate L_(i). In the case of sinusoidal oscillation of the rotor R₁ and left-hand rotation of R₁ in θ(−90°, +90°) with change of the angle θ of the crank to (0°, 180°) and of the corresponding angle ω of the rotor the mechanism gives the following results: (1) for θ−0 and ω=0 the four plates L_(i) of the valves V₁ are in closed position and velocity ω>0 of R₁ is maximum. An increase of θ causes coupling of the toothings (D₁, d₁) and (D₂, d₂) and beginning of the opening phase which terminates for 0=0 and and ω=ω₁ with a tangential position of L₁ and L₂ with respect to the longitudinal axis of C₁. At the same time the blades L₃ and L₄ remain in the closing position. (2) for θ=90° and ω=ω_(o) the left-hand force f₁>0 is maximum and velocity ω′ of R₁ is null. (3) With an increase in θ rotor velocity is ω′<0 and a force f_(i>)0 until for θ=180°−θ₁ and ω=ω₁ uncoupling of the toothing (D₁, d₂) and (D₂, d₂) starts. (4) For θ=180° and ω=0 and a maximum right-hand velocity ω′<0 the coupling of the toothing (D₁, d₁) and (D₂, d₂) ends, closing of the blades L₁ and L₂ is completed and coupling of the toothing (D3, d₃) and (D₄, d₄) initiates. (5) for θ=180°+θ₁ and ω=−ω₁ the plates have reached the tangential position with respect to the axis of the circuit C₁. (6) for ν=270° and ω=−ω_(o) the right-hand force f_(1′)<0 is maximum and velocity ω′ null. (7) To an increase in θ corresponds a 107 ′>0 and f₁<0 until the uncoupling phase of the toothing (D₃, d₃) and (D₄, d₄) initiates for θ=360°−θ₁ and ω=−ω₁ which terminates for 0=360°, ω−0, maximum velocity ω′>0 and plates L₃ and L₄ in closing position.

[0050] It is noted that the closing and opening operation of the valves V₁ takes place with the rotation of a very small angle ω₁ because of the very high axle ratio (radius r_(o) of C₁ /radius of a₁). In addition the baricentric position of the shafts a₁ cancels the moment generated thereon by the motion of the liquid and reduces their stress. To avoid hydraulic leaks stuffing boxes are arranged at the crossings of the circuits C₁ and C₁, by the shafts 1 and 1′.

[0051] E) Inertial Forces Employed in the Liquid of the Turbopump and Balancing of the reactions Transmitted to the Supporting Framework

[0052] With reference to the above statements the inertial forces employed in the operation of the turbopump (FIG. 3/5) are of two types, to wit: (a) the pair of rotational inertial forces f₁ and f_(1′) with identical semisinusoidal trend. The f₁ has a left-hand direction and is generated in θ (0°, 180°) in the liquid of C₁ by a change in the velocity of R₁ from a maximum left-hand value to a maximum right-hand value. The f_(1′) has a right-hand direction and is generated in θ (0°, 180°) in the liquid C_(1′) by an equal and opposite change in velocity of R₁. (b) The pair of impulsive inertial forces f_(CH) and f_(CH′) corresponding to the closing of the valves of the circuits C₁ and C_(1′) at the end of the above mentioned intervals and the sudden stopping of the relative velocity of the liquid of the circuits C_(1′) which has reached maximum value and in addition is concomitant with a maximum rotating velocity and same direction as the rotor. The forces f_(CH) are useful because they return to the rotor the kinetic energy of the velocity of the liquid and because they equalize the trend of the inertial forces f_(i) at the points where they are null (FIG. 3/5).

[0053] Balancing of the reactions to the inertial forces due to the oscillatory motion of the rotor and transmitted to the supporting framework can be obtained by using a flywheel having a moment of inertia identical to that of the rotor R₁ with respect to an axis of rotation parallel to that of R₁. It must also be subjected to oscillatory motion which differs only for a phase difference of 180° with respect to the phase of the rotor to be balanced.

[0054] (F) The Turbopump Connected to a Filling Tank and a Drain Tank

[0055] It consists (FIG. 4/5) of a machine identical to the one shown in FIG. 1/5. In it the section S_(A) is connected by a tube to a filling tank S_(C) arranged at a geodetic height and which develops the pressure P_(e) and the external force applied to the machine f_(e)=p_(e)S_(A). The external force f_(e) can also be developed by a pump whose outlet is connected to the section S_(A). In particular the pump can be based on rotational inertial forces. The section S_(B) is connected by a tube to a drain tank S_(S). Oscillation of the rotor R₁ is caused by a connecting rod & crank system as designed or by a shaft system a_(MA) to which is applied a bearing in eccentric position whose external ring rotates between two blades fastened to R₁ as described above. Oscillation of the rotor R₁ generates the inertial forces whose mean value — and in case of sinusoidal oscillation of the rotor— is as above {overscore (f)}_(i)=8πm _(o)φ_(o)r_(o)n² indicated. The machine operates as a turbine or as a pump depending on whether the rps of the crankshaft of mean value equal to f₁ viz. {overscore (f)}_(i) is less or more than n=n_(o)=(f_(e)/m_(o)φ_(o)r_(o)){fraction (1/2)}. Operation of the machine as a turbine allows conversion of the potential pressure energy accumulated in the tank S_(C) into mechanical energy of the crank a_(MA) and allows use of said energy for mechanical purposes. A motor applied to the shaft B_(MA) with n>n_(o) allows operation of the machine as a pump to transfer the liquid from the tank S_(S) to the tank S_(C) to create a reserve of energy which can be used later.

[0056] G. Control of the Power Exchanged Between a Motor and a User

[0057] Control of the power exchanged between the shaft a_(MO) of a motor MO and the shaft a_(UT) of a user UT implies the following two problems: (a) control of the power transmitted by the shaft a_(MO) to the shaft a_(UT), and (b) control of the power transmitted from the shaft a_(UT) to the shaft a_(MO) and its utilization.

[0058] If it is {overscore (f)}_(j)−{overscore (f)}_(i)>0 where j=2, 2′ and i=1, 1′ (FIG. 5/5) there is a right-hand velocity ν_(c) of the liquid contained in the circuit of which the sections S_(A1), S_(B1), S_(B2) and S_(AZ) are parts. Accordingly the machine M_(A2) operates as a pump which converts the mechanical power of the shaft a_(MO) of the motor MO into hydraulic power which is transferred to M_(A1) operating as a turbine. The latter converts the hydraulic power into mechanical power which is transferred to the shaft a_(UT) of the user UT.

[0059] Designating by n₁ and n₂ respectively the number of rps of the shafts a_(UT) and a_(MO) it can be stated that, (a) the machine M_(A1) develops power null for n₁=0 and for n₁=n₂ while for n₁ satisfying to 0<n₁<n₂ we have:

P={overscore (f)} _(i) {overscore (ν)} _(c) +P _(CH)≠

[0060] where is

{overscore (f)} _(i)=8πm_(o)φ_(o) r _(o) n ₁ ²

[0061] and

{overscore (ν)}=K(n ₂ −n ₁);

[0062] (b) that the machine M_(A1) for n₁=n_(m) where n_(1<n) _(m<n) ₂ develops a maximum power P_(M) and accordingly the moment applied to the shaft by the user M_(UT)=P/2n′n₁ in the interval n₁(0, n_(M)) increases with the increase of n₁ while it decreases with the increase of n₁ in n₁(n_(M), n₂).

[0063] Accordingly the M_(A1) for {overscore (f)}₂{overscore (f)}₁>0 develops an ideal moment for connection of any motor to any user.

[0064] For {overscore (f)}₂{overscore (f)}₁<0 the machines M_(A2) and M_(A1) operate respectively as a turbine and a pump and accordingly the mechanical power connected to auT is transmitted to a_(MO). In this case the corresponding energy, if the phenomenon is of brief duration, can be stored in fly-wheel weights. If the phenomenon is of long duration it can be used with other suitable systems.

[0065] Change of sign of the relationship {overscore (f)}₂−{overscore (f)}₁ can be accomplished be merely changing the number of rps of MO. In addition the series of two machines MA₂ and MA₁ is allowed even in the presence of an even very high ratio of their oscillation frequency and without the need of a speed reducer.

[0066] The system can be particularly advantageous in the field of automobile traction by replacing the speed change gear with toothed wheels having a limited number of ratios and requiring in addition a clutch and an appropriate control with the above described system having an automatic and continuous control. {overscore (f)}₂−{overscore (f)}₁>0 in addition as assumed above in para. (b) the system proposed can even avoid the dispersion of energy with {overscore (f)}₂−{overscore (f)}₁<0 more or less extended braking as it can be appropriately used after its transfer to the drive shaft. 

1. Machine based on rotational inertial forces operating as a turbine or a pump characterized in that it consists of the following components, to wit, (a) a mechanism made up of a crankshaft, crank and connecting rod designed to generate the oscillatory motion of the rotor R₁, (b) a tube fastened to R₁ curved and closed on itself and communicating with an inlet S_(A) and an outlet S_(B) dividing the tube in two circuits C₁ C_(1′) in such a manner that the surface area of their projection on a plane perpendicular to the oscillation axis of R₁ is equal, (c) four 2-way valves each inserted at each end of C₁ and C_(1′) and operated by a mechanism in which with to complete oscillation of R₁ corresponds a left-hand rotation of 360° of the cranks causing opening of the pair of valves of C₁ only in the interval θ(0°, 180°) and opening of the valves of C_(1′) only in the interval θ(180°, 360°) with the origin of the angle θ being fixed so that for θ=0° there is a corresponding maximum left-hand velocity of the rotor and for θ=180° the maximum right-hand velocity. In this manner the liquid of C₁ develops a left-hand inertial force f₁ and the liquid of C_(1′) an identical right-hand inertial force f_(1′). In addition both are oriented towards the cross section S_(A) to which is applied the external force f_(e) with opposite direction with the forces f_(i) increasing with the velocity of rotation of the cranks so that for a mean value f_(i) less than f_(e) the velocity of the liquid of C_(i) has a direction from S_(A) to S_(B) and the machine operates as a turbine while for {overscore (f)}_(i)>{overscore (f)}_(e) the machine it operates as a pump.
 2. Machine in accordance with claim 1 characterized in that the valve opening and closing mechanism consists of the following components, to wit, a shaft parallel to that of the rotor R₁ rotating in baricentric position in C₁ on bearings fastened to R¹ to the outside of C₁ and having a side toothing and a blade fastened to said shaft in the active circuit to realize opening and closing of the valve; a cylinder segment fastened to the supporting frame with a toothing which for reciprocal motion of R₁ couples for a short arc with the above mentioned side toothing with all being arranged in such a manner that with each 180° rotation of the crankshaft the above mentioned shaft in rotating with the rotor in an angle ±φ₀ and coupling with the toothing of the cylindrical segment at the beginning and the end of the angular path causes alternately rotation by ±90° of the valve closing and opening member with an identical mechanism being provided for each valve.
 3. Machine in accordance with claim 1 characterized in that the closing and opening member of the active circuits consists of a blade fastened to a rotating shaft in a position such that the moment generated on said shaft by the liquid of the circuit is null.
 4. Machine in accordance with claim 1 characterized in that the reactions transmitted to the supporting frame and caused by the inertial force of the oscillatory motion of R₁ are balanced by a flywheel having inertial moment identical to that of R₁ and subjected around an axis parallel to that of R₁ to an oscillatory motion differing from that of R₁ only by a 180° phase difference.
 5. Machine in accordance with claim 1 characterized by the system consisting of the series Filling tank S_(c)-turbopump-Drain Tank S_(s) with the machine operating as a turbine with a number of revolutions per second of the crankshaft n<n_(o) for which the mean value of the inertial forces developed in the active circuits of the machine is less than the external force generated by the geodetic height of the filling tank S_(c) with the turbine in this condition converting the liquid pressure energy of the tank S_(c) into mechanical energy of the user employing an ideal moment decreasing with the increase in the number of revolutions per second of its shaft with the liquid used being dumped at the same time into the drain tank S_(s) with a motor applied to the crankshaft with a number of revolutions per second n>n_(o) causing operation of the machine as a pump and transfer of the liquid from the tank S_(s) to the tank S_(c) to constitute an energy reserve usable subsequently.
 6. Machine in accordance with claim 1 characterized by the series of two machines M_(A2) and M_(A1) with cross sections (S_(A2), S_(A1)) and ( S_(B1), S_(B2)) connected hydraulically and with crankshafts of M_(A2) and M_(A1), connected respectively by means of connecting rods to the shaft of the motor a_(MO) and of the user a_(UT) for {overscore (f)}₂−{overscore (f)}₁>0 with the machine M_(A2) operating as a pump transmitting power of the motor MO converted into hydraulic power to the machine M_(A1) operating as a turbine while the turbine converts the hydraulic power into mechanical power and transmits it to the user by employing a moment decreasing with the increase in revolutions per second and the above mentioned series being able to replace advantageously any geared speed changer with in addition the series for {overscore (f)}₂−{overscore (f)}₁<0 transferring to the motor the kinetic energy of the user which can be appropriately utilized.
 7. Machine in accordance with claim 1 characterized by connection of the two machines M_(A2) and M_(A1) which exchange the hydraulic and mechanical power even in the presence of a very high ratio of the two frequencies of their oscillatory motion giving the advantage of avoidance of the use of a speed reducer. 